Let W1 and W2 be subspaces of a vector space V with W1 ( W2 = {0}. Let W1 + W2 be as defined in Exercise 34. Suppose that V = W1 + W2. Prove that every vector in V can be uniquely written as w1 + w2, where w1 is in W1 and w2 is in W2. In this case we write V = W1 W2 and say that V is the direct sum of the subspaces W1 and W2.